Sunday, March 04, 2007

The terrible cost of moving electricity

Wind, solar, and hydro electrical generation are all intermittent fluctuating power sources that require long distance power lines to transfer the generated power to end users. It's a little difficult to know how feasible it is to transmit power across thousands of miles. On the one hand, it's obvious that if you make the conductors thick enough, you can reduce the losses as much as you like. On the other hand, it isn't done already on the massive scale necessary to support intermittent fluctuating power sources.

Now lets consider how much wire we need to move 10 gigawatts across 1000 miles. The more wire (cross section) we use, the less resistance we'll have and the less power will be lost. The optimal point for these kinds of problems is when the marginal cost of the wire is equal to the marginal cost of the electricity lost to resistance. After this point, when you add wire, the cost of the wire increases faster than the value of the power saved, so that you have lost money.

Let's assume the electricity costs $0.04/kw-hr and that we're transmitting an RMS average of 10 gigawatts. The RMS (root mean square) part of this last assumption lets us estimate power losses. Finally, lets assume we transmit with a +/- 500 kV high-voltage DC transmission system, which is the lowest-loss long-distance transmission system available today.

To convert ongoing electrical costs into a present value we can compare to the cost of the wire, assume a discount rate of 5%.

The optimal point for 10 GW is 4 conductors each way (8 total conductors).

wire cost: $366 million

resistance: 8.72 ohms

power lost: 871 megawatts

P.V. lost electricity: $305 million

Here the wire cost doesn't quite equal the present value of the lost electricity because the number of conductors is quantized, and I'm only considering one type of conductor. But, it's close.

One interesting thing about electrical transmission is that the optimal point for wires used doesn't change with distance. Double the distance, double the resistance, double the power lost, and double the wire cost. The total cross section of conductors used is the same. So we can talk about how much more electricity costs after it has moved a distance.

The electricity transmitted has three costs: the cost of the power lost, the rent on the money borrowed to build the transmission lines, and the maintenance and depreciation on the power lines. We just showed the first two will be equal, and the last will be smaller - electric power lines are like dams and bridges, they last for a long time. So the total cost of transmission will be a bit more than twice the cost of the power lost.

This is a really nice rule of thumb because it reduces away the actual costs of power and interest rates and so forth. We can now convert a distance into a cost multiplier. For the geeks among you, the multiplier is (1+power lost)/(1-power lost). Note that power lost is a function of the relative costs of copper and electricity, so that hasn't been reduced away, but merely hidden.

After 1000 miles, 8.71% is lost, and delivered power costs at least 19% extra.After 2000 miles, 17.4% is lost, and delivered power costs at least 42% extra.After 3000 miles, 26.1% is lost, and delivered power costs at least 71% extra.After 4000 miles, 34.8% is lost, and delivered power costs at least 107% extra.

This, in a nutshell, is the argument for locating generators near their loads.

There is a hidden assumption above: that the average power distributed (this goes in the denominator for loss%) is equal to the RMS power distributed (this goes in the numerator for loss%). If the power transmitted is peaky, like from an intermittent wind farm, then the average power will be smaller than the peak power, the power lost % grows, and delivered power costs even more.

Delivered costs are actually even worse: typically, when a transmission line is built, its capacity isn't used immediately. In the years until the capacity is reached, you pay for the capacity you are not using. In fact, you always want some reserve capacity, which drives the price up even more.

So, there you have it. If you spread your wind farms over the whole continent, and interconnect them with a high-capacity power grid, then the cost of that power once delivered is substantially more than the cost of producing it. Not only does wind power have to be as cheap as coal, even after you divide by availability, but it has to overcome the extra and substantial cost of distribution.

And the same goes for solar and hydro too.

I'll leave with a note of hope. Hydro ended up being cheap enough that the cost of distribution could be overcome. Maybe solar or wind can get that cheap as well.

7 comments:

That's a nice article and well researched, but if I remember my basic engineering courses on power transmission correctly: The majority of the power transfered in high V lines is through either the skin effect or through the actual EMF that surrounds the wire. Very little current flows through the wire. (Unless you were talking total impedance rather than resistance). Additionally, I do not believe anyone uses DC power transmission.

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At 60 Hz, the skin depth is 8.57 mm, which means that Southwire probably doesn't sell a lot of 47.8 mm diameter Joree cable into the AC transmission market. I think high-capacity long distance AC uses those funky wires you see where two or three smaller wires are held spaced apart by a few inches, to make a kind of Litz wire.

No significant portion of the current is carried through EMF around the wire.

Lots of folks use high voltage DC transmission. Check the wikipedia article, it has a list of installations that goes on for pages, including dual 3000 MW HVDC links out of the Three Gorges Dam.

I get the sense your first posting was a piece of junk so I wouldn't dump your second posting, which seems to be a repost of something from some other guy, Keith G Kato. If you were trying to increase your credibility so that I'd be more impressed with Heinlein fandom, it didn't work. I've read a bit of Heinlein, and actually referenced The Moon is a Harsh Mistress just the other day at work, but I'm not much into fandom. Have fun and brush up on your basic engineering.

Attempting to understand the marginal costs of transporting wind or solar energy as compared with generating power through fossil fuels locally is a worthy discussion.

Is it possible to include in this analysis the deferred costs of pollution cleanup, disease management, healthcare impact, human death, and expired renewability as "hidden" costs that today are borne by future generations, as compared with the costs borne by current energy consumers?

There are two problems with trying to quantize the deferred costs of all the nastiness associated with fossil fuel burning.

The first is that we don't have much experience with the activities that we are committing ourselves to in the future. If you want to know how much a pound of steel will cost in 20 years, you can actually get a decent estimate. If you want to know how much it will cost to build a coal-burning plant which conforms to then-current pollution regulations... (shrug). If those regulations are applied to older plants built now, how much will the retrofit cost? (shrug)

Health effects have a twist which makes thing potentially even harder to estimate. If extra ozone causes 50 more asthma sufferers a year to die, that might actually save the money of their future health care. I'm not saying that's a good thing, I'm saying that it's hard to quantify the costs.

The second problem is that you have to associate a discount rate to any cost in the future. Then it turns out your analysis is always more sensitive to this discount rate than to anything else, and there is no consensus about how to set the discount rate. The economic literature could really use a breakthrough in this area, because it stymies all sorts of long-range planning.

As I point out in the last paragraph, one of the interesting results of the analysis is that, if renewable energy gets cheap enough, it can be transported farther. There isn't actually a hard economic limit to how far electricity can go. So if wind power gets cheap enough (relative to fossil fuels), we really will be able to build continent-wide grids.

One other thing that can mitigate the cost of moving wind power, both variable and baseload, is wind-local generation of high-energy products. Shipping hydrogen around is total stupidity, but hydrogen isn't the only high-energy product you might ship. Ammonia comes to my mind as a product which is already shipped across vast distances, whose primary cost comes from the energy to make it, and which has a potentially low capital cost for the generation equipment. You can imagine intermittent ammonia generators near clusters of wind turbines which serve to soak up otherwise untransmittable power peaks into a tank of valuable stuff that can be used on nearby farms.

Sorry to necro this 5 year-old post, but I'm curious if the technology has changed much since then?

Desertec claims ( http://www.desertec.org/concept/technologies/ ) that "The line losses are very low – only around three percent per 1000 kilometers – and the extra cost is only one or two cents per kilowatt hour."

Have there been advances in the HVDC realm, or are they fudging the numbers?

One thing I didn't analyze in this post is the effect of raising the transmission voltage. Doubling the voltage reduces the losses by a factor of 4, but increases the insulation and switching costs by a factor of two to four. I think the biggie here is the switching costs, and I suspect those are coming down slowly.

So, things have changed a bit in the last five years. A quick check of http://en.wikipedia.org/wiki/List_of_HVDC_projects shows the following projects at 500kV or higher. Five years ago 500kV was the upper limit.

What has changed? The Three Gorges Dam came online, Siemens got +/-800kV equipment practical, shipping coal by rail became even more expensive due to the rising price of oil, and China's economy grew by 118% (OMG!). All of these events are intercausal. The analysis I posted elsewhere, that shows it is cheaper to move energy by wire than by rail, is even more true today. And since China's cities aren't located on top of their coal mines, they are moving some really big power long distances.

Desertec's statement you reference is naiive. Their whole agenda sounds like a German green fantasy fed by North African oil barons who are thinking about what they will do when their wells dry up. Consider power from El Oued, Algeria to Munich, which is at minimum 1700km and will be more like 2000km for a feasible route. An 800kV line would be appropriate. Losses will be 11% and delivered electricity will cost 25% more at the destination than the source. The inverters at each end will cost even more, so maybe the overall charge is +40%.

I can believe that locally-mined coal power in El Oued might be 40% cheaper than coal power in Munich. For one thing, Germany is currently set to burn *all* of their domestic coal in the next 30-40 years. After that, locally mined power nearly anywhere will be cheaper than Germany's gas turbines burning Russian gas.

Solar and wind power are currently significantly more expensive than coal. Desertec appears to be selling the hope that they will become more than 40% cheaper than coal. I see no reason to expect this outcome. A more likely future is that France will pick up the money by increasing their nuclear-sourced power exports to Germany.